Pulsed FM radar is a form of radar that detects targets using a pulsed frequency modulated signal. The use of a pulsed frequency modulated signal provides better range resolution and signal-to-noise ratio than other types of signals. Various types of pulsed frequency modulated signals may be used such as a pulsed linear chirp signal (a pulsed sinusoidal signal having a frequency that changes linearly with time), a pulsed non-linear chirp signal (a pulsed sinusoidal signal having a frequency that changes non-linearly with time), and a pulsed phase-coded signal (a pulsed sinusoidal signal that is phase-modulated in accordance with a binary code).
A pulsed FM radar receiver extracts information about a target from a received pulsed FM radar signal by passing the signal through a matched filter. A matched filter is commonly implemented in the frequency-domain by transforming samples of the received pulsed FM radar signal into a frequency domain spectrum, multiplying the spectrum with the complex conjugate of a frequency-domain estimate of the transmitted pulsed FM radar signal, and transforming the result back into the time-domain. This process “de-spreads” or “compresses” the received pulsed FM radar signal into a narrow pulse, and for this reason it is referred to as “pulse compression.” For more information on pulse compression see section 5.3 of “Simulations for Radar Systems Design” by Bassem R. Mahafza and Atef Z. Elsherbeni, Champman & Hall/CRC Press, 2003.
An “impulse response” of a pulsed FM radar transmitter, also referred to as the “point spread function,” is an important quality measurement. The impulse response is the brightness pattern of an image produced after pulse compression from a pulsed FM radar signal that is received directly from a pulsed FM radar transmitter or reflected from a very small point target. A good impulse response has a large value corresponding to the location of a target and small values for all surrounding locations. In other words, the impulse response describes the spatial resolution of a pulsed FM radar system.
A common impairment of an impulse response is a secondary or “ghost” response. A ghost response is created when a pulsed FM radar transmitter transmits not only an intended or “main” signal but also a “ghost” signal, that is, a copy of the main signal that is lower in amplitude than the main signal and delayed relative to it. A ghost signal is commonly caused by a low-level internal reflection within the pulsed FM radar transmitter. After pulse compression, the ghost signal results in a fictitious pulse at a location not corresponding to a target referred to as a ghost pulse or ghost response. A ghost pulse can interfere with the proper operation of a radar system by giving a false indication of a second target when one is not present, or alternatively, by obscuring the reflection of a second target when one is present. For these reasons, it is important to accurately characterize the impulse response of a pulsed FM radar transmitter and calibrate the corresponding pulsed FM radar receiver accordingly.
Test and measurement instruments including real-time spectrum analyzers such as the RSA6000 Spectrum Analyzer Series and real-time oscilloscopes such as the DPO/DSA70000B Digital Phosphor Oscilloscope Series, both of which are available from Tektronix, Inc. of Beaverton, Oreg., can be used to measure the impulse response of a pulsed FM radar signal. These test and measurement instruments acquire samples of the pulsed FM radar signal using an acquisition system, perform pulse compression on the acquired samples using software or digital signal processing circuitry, and present a visual image of the resulting impulse response on a display. However, before performing pulse compression, these test and measurement instruments must first apply a window function to the acquired samples in order to avoid truncating the pulsed FM radar signal and thereby generating side-lobes in the frequency domain, an effect referred to as “spectral leakage.” The window function is centered about the main signal and thus attenuates the main signal properly. However, if the pulsed FM radar signal includes a ghost signal, then because the ghost signal is delayed relative to the main signal, the ghost signal is not located within the center of the window function but is rather located within a portion of the window function having reduced amplitude, and thus the window function truncates the ghost signal. This truncation of the ghost signal, after pulse compression, causes these test and measurement instruments to inaccurately report the amplitude of the ghost pulse relative to the amplitude of the main pulse.
What is desired is a method of measuring the impulse response of a pulsed FM radar signal that provides a more accurate measurement of the amplitude of a secondary response relative to the amplitude a main response.